Problem: Reduce to lowest terms: $ \dfrac{4}{5} \div \dfrac{4}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{4}{9}$ is $ \dfrac{9}{4}$ Therefore: $ \dfrac{4}{5} \div \dfrac{4}{9} = \dfrac{4}{5} \times \dfrac{9}{4} $ $ \phantom{ \dfrac{4}{5} \times \dfrac{9}{4}} = \dfrac{4 \times 9}{5 \times 4} $ $ \phantom{ \dfrac{4}{5} \times \dfrac{9}{4}} = \dfrac{36}{20} $ The numerator and denominator have a common divisor of $4$, so we can simplify: $ \dfrac{36}{20} = \dfrac{36 \div 4}{20 \div 4} = \dfrac{9}{5} $